On the eve of a problem-set due date, a professor receives an e-mail from one of her students who claims to be stuck on one of the problems after working on it for more than an hour. The professor...

On the eve of a problem-set due date, a professor receives an e-mail from one of her students who claims to be stuck on one of the problems after working on it for more than an hour. The professor would rather help the student if he has sincerely been working, but she would rather not render aid if the student is just fishing for hints. Given the timing of the request, she could simply pretend not to have read the e-mail until later. Obviously, the student would rather receive help whether or not he has been working on the problem. But if help isn’t coming, he would rather be working instead of slacking, since the problem set is due the next day. Assume the payoffs are as follows:

(a) What is the mixed-strategy Nash equilibrium to this game?

(b) What is the expected payoff to each of the players?